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Simplifying (x + 3)(2x + -5) + (2x + -5)(2x + -5) = 0 Reorder the terms: (3 + x)(2x + -5) + (2x + -5)(2x + -5) = 0 Reorder the terms: (3 + x)(-5 + 2x) + (2x + -5)(2x + -5) = 0 Multiply (3 + x) * (-5 + 2x) (3(-5 + 2x) + x(-5 + 2x)) + (2x + -5)(2x + -5) = 0 ((-5 * 3 + 2x * 3) + x(-5 + 2x)) + (2x + -5)(2x + -5) = 0 ((-15 + 6x) + x(-5 + 2x)) + (2x + -5)(2x + -5) = 0 (-15 + 6x + (-5 * x + 2x * x)) + (2x + -5)(2x + -5) = 0 (-15 + 6x + (-5x + 2x2)) + (2x + -5)(2x + -5) = 0 Combine like terms: 6x + -5x = 1x (-15 + 1x + 2x2) + (2x + -5)(2x + -5) = 0 Reorder the terms: -15 + 1x + 2x2 + (-5 + 2x)(2x + -5) = 0 Reorder the terms: -15 + 1x + 2x2 + (-5 + 2x)(-5 + 2x) = 0 Multiply (-5 + 2x) * (-5 + 2x) -15 + 1x + 2x2 + (-5(-5 + 2x) + 2x * (-5 + 2x)) = 0 -15 + 1x + 2x2 + ((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) = 0 -15 + 1x + 2x2 + ((25 + -10x) + 2x * (-5 + 2x)) = 0 -15 + 1x + 2x2 + (25 + -10x + (-5 * 2x + 2x * 2x)) = 0 -15 + 1x + 2x2 + (25 + -10x + (-10x + 4x2)) = 0 Combine like terms: -10x + -10x = -20x -15 + 1x + 2x2 + (25 + -20x + 4x2) = 0 Reorder the terms: -15 + 25 + 1x + -20x + 2x2 + 4x2 = 0 Combine like terms: -15 + 25 = 10 10 + 1x + -20x + 2x2 + 4x2 = 0 Combine like terms: 1x + -20x = -19x 10 + -19x + 2x2 + 4x2 = 0 Combine like terms: 2x2 + 4x2 = 6x2 10 + -19x + 6x2 = 0 Solving 10 + -19x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (2 + -3x)(5 + -2x) = 0Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {0.6666666667, 2.5}
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